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Unformatted text preview: seful for reducing or dealing with complexity
when applying the theory.
What does probability mean? If I roll a fair six-sided die, what is the probability a six shows?
How do I know? What happens if I roll the same die a million times?
What does it mean for a weather forecaster to say the probability of rain tomorrow is 30%?
Here is one system we could use to better understand a forecaster, based on incentives. Suppose
the weather forecaster is paid p (in some monetary units, such as hundreds of dollars) if she declares
that the probability of rain tomorrow is p. If it does rain, no more payment is made, either to or
from the forecaster. If it does not rain, the forecaster keeps the initial payment of p, but she has
to pay − ln(1 − p). In view of these payment rules, if the weather forecaster believes, based on all
the information she has examined, that the probability of rain tomorrow is q , and if she reports
p, her expected total payoﬀ is p + (1 − q ) ln(1 − p). For q ﬁxed this payoﬀ is maximized at p = q.
That is, the for...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.
- Spring '08
- The Land